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Zbl 0966.65056
He, Ji-Huan
A review on some new recently developed nonlinear analytical techniques. (English)
[J] Int. J. Nonlinear Sci. Numer. Simul. 1, No.1, 51-70 (2000). ISSN 1565-1339

Summary: This paper is a survey of some recent developments in nonlinear analytical techniques, which covers mainly the following 6 categories: 1) variational iteration method, 2) homotopy perturbation method, 3) linearized perturbation method, 4) parameterized perturbation method, 5) various modified Lindstedt-Poincaré methods, and 6) modified Adomian decomposition method. Each of those methods can be an effective procedure for analytical solutions of a wide class of both weakly and strongly nonlinear systems without small parameter assumption. Some of these new technologies have never appeared in any other literature. The emphasis is put upon the author's recent work, and the references are not exhaustive.

MSC 2000:: *65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general
65-02 Research monographs (numerical analysis)
34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

Keywords: survey paper; Lagrange multiplier; Duffing equation; variational iteration method; homotopy perturbation method; linearized perturbation method; parameterized perturbation method; Lindstedt-Poincaré methods; Adomian decomposition method; nonlinear systems

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